RMS levels and perceived volume are more important than peak levels and absolute headroom.
If you were to push the average level up so that the highest peaks got closer to, say, -0.5 to -1 dB, the final volume might be excessive. If the final destination is a CD, that may be perfectly OK. But if your material is subsequently reprocessed by iTunes, YouTube or radio, it could be harmed if you've pushed the levels too high.
Personally, I like to see occasional peaks getting up around -0.5 dB, but only if doing so doesn't increase average RMS beyond my target. If my overall volume is already where I want it to be, but the peaks seem low, I'll check for excessive drum compression/limiting and maybe let the drums pop out more.
But that assumes highly-percussive material. If it was acoustic folk or orchestral music, I'd be quite happy with -2.4 dB peaks.